"wire_mat_gui" add-on, how to render wireframe with visible edges only?
I wasn't able to produce a satisfactory render using that addon. I'm not sure if it's a bug in how the script was written, or if it's a bug in Blender, but I noticed that the extra edges show up when you move around in the viewport. If you access the material settings, and modify some of the values of the material, the extra lines disppear until you move in the viewport again. 

That being said, rendering a mesh with its wireframe can be accomplished using Blender's built-in modifiers. Start with the default scene, and subdivide the mesh a few times:



Next, tab back into object mode, and scroll to the "Modifiers" tab. Click "Add Modifier" and choose "Wireframe":



When you do this, the mesh will change to show only the wireframe. However, you want to have the original mesh and the wireframe, so uncheck "Replace Original" in the modifier panel:



Next, scroll to the "Materials" tab, and add a new material to your object. This material is going to be the material for the wireframe. So now, you should have two materials, the default material, and the material you just added. Change the new material to whatever you want, in this case, I've created a red material:



Finally, scroll back to the "Modifiers" panel, and increase the "Material Offset" to "1". An offset of 1 will mean that the wireframe uses the second material from the material tab. So, if you had a bunch of other materials applied to your object, and the material you wanted to use for the wireframe was the 10th material in your list of materials, you would set "Material Offset" to "9". Now if you render, the wireframe will be rendered using the new material you created, and the cube will be rendered using the default material:



Does that help at all?